Question

If ${\sin }^{-1}x+{\sin }^{-1}y=\frac{\pi }{2}$, then ${\cos }^{-1}x+{\cos }^{-1}y$ is equal to

• A. $\frac{3\pi }{4}$
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is C $\frac{\pi }{2}$

Given : ${\sin }^{-1}x+{\sin }^{-1}y=\frac{\pi }{2}\cdots \left(1\right)$
We know that,
${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}\Rightarrow {\sin }^{-1}x=\frac{\pi }{2}-{\cos }^{-1}x$

$\therefore$ Equation $\left(1\right)$ becomes
$\frac{\pi }{2}-{\cos }^{-1}x+\frac{\pi }{2}-{\cos }^{-1}y=\frac{\pi }{2}\Rightarrow {\cos }^{-1}x+{\cos }^{-1}y=\frac{\pi }{2}$